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The Modification Puzzle of Mandarin Numeral Phrases

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Abstract

To appear in Proccedings of SuB 29
The Modification Puzzle of Mandarin Numeral Phrases1
Jia REN University of Massachusetts Amherst
Qiuhao Charles YAN Queen Mary University of London
Satoru OZAKI University of Massachusetts Amherst
Abstract. It has been observed in the literature that the nominal-internal word order influences
the specificity in Mandarin Chinese (Huang, 1982; Tang, 1990; Yang, 2005; Partee, 2006;
Zhang, 2006). In this paper, we concentrate on numeral phrases that contain modifiers and
show how their interaction displays the interpretational difference. We propose a semantic
solution that consists of two resources, namely (i) the semantics of classifiers from Japanese
(Sudo, 2016), and (ii) the semantics of relative clauses from Turkish (Sa ˘
g, 2019). We show that
this specificity contrast is pervasive in Mandarin nominal constructions that deserve a uniform
account.
Keywords: numeral constructions, specificity, modification, (in)definiteness, cardinality
1. Introduction
When a Mandarin nominal contains a numeral and a modifier, the relative word order between
the numeral and modifier controls the specificity and uniqueness of the nominal. Consider
specificity first. The effect of nominal-internal word order on specificity has been noted in the
literature (Huang, 1982; Tang, 1990; Yang, 2005; Partee, 2006; Zhang, 2006). Zhang (2006)
observes that numeral phrases with prenumeral modifiers (Mod-Num phrases) are unambigu-
ously specific. For instance in (1a), the relative clause lai shang ke (de) ‘that/who attended
class’ precedes the numeral (and the classifier) san (ge) ‘three (CL)’, and the nominal receives
a specific interpretation. On the other hand, numeral phrases with postnumeral modifiers (Num-
Mod phrases) are usually nonspecific (1b); a specific interpretation is forced by an anaphoric
use of the nominal.
(1) a. Modifier-Numeral-Classifier-Noun (Mod-Num phrases)
lai
come
shang
attend
ke
class
de
DE
san
three
ge
CL
xuesheng
student
‘the three students who regularly attended class’ [specific]
b. Numeral-Classifier-Modifier-Noun (Num-Mod phrases)
san
three
ge
CL
lai
attend
shang
class
ke
DE
de
student
xuesheng
‘three students who regularly attended class’ [non-specific]
The specificity contrast can be diagnosed using various constructions. For example, existen-
tial constructions of the form lai le + nominal + predicate” require the nominal part to be a
nonspecific indefinite (Li and Thompson, 1981; Huang, 1987, among others). As expected,
Num-Mod phrases can appear in this construction (2a), while Mod-Num phrases cannot (2b).
(2) Existential construction (Zhang, 2006)
a. Num-Mod phrase
Lai-le
come-PFV
san
three
ge
CL
dai
wear
yanjing
glasses
de
DE
xuesheng
student
hen
very
haoxiao.
funny
1We would like to thank abc, native speakers def. . .
Jia Ren—Qiuhao Charles Yan—Satoru Ozaki
‘Three students who wear glasses have come. They are very funny.’
b. Mod-Num phrase
Lai-le
come-PFV
dai
wear
yanjing
glasses
de
DE
san
three
ge
CL
xuesheng
student
hen
very
haoxiao.
funny
Intended: ‘The three students who wear glasses have come. They are very funny.’
Extractions are allowed from non-specific nominals, but not from specific nominals (Enc¸, 1991;
Diesing, 1992). Zhang (2006) shows that Mod-Num nominals (3b), but not Num-Mod nomi-
nals (3a), pattern like specific nominals in this regard.
(3) Topicalisation (Zhang, 2006)
a. Num-Mod phrase
Lishi-shu
history-book
Akiu
Akiu
(xingkui)
fortunately
du-guo-le
read-EXP-PRF
liang
two
ben
CL
guanyu
about
Xizang
Tibet
de
DE
t.
Akiu has (fortunately) read two history books on Tibet.
b. Mod-Num phrase
Lishi-shu
history-book
Akiu
Akiu
(xingkui)
fortunately
du-guo-le
read-EXP-PRF
guanyu
about
Xizang
Tibet
de
DE
liang
two
ben
CL
t.
Intended: ‘Akiu has (fortunately) read the two history books on Tibet.’
Another diagnostic comes from scope interactions. A universal quantifier shows scope ambi-
guity with a Num-Mod phrase: the universal quantifier may take wide or narrow scope (4a). A
universal quantifier does not show scope ambiguity with a Mod-Num phrase (4b). The contrast
shows that Mod-Num phrases are not quantificational, and do not take scope; this is in line with
their obligatorily specific interpretations.
(4) a. Num-Mod phrase [>3 : ;3 >:]
Mei
Every
ge
CL
ren
people
dou
DOU
renshi
know
san
three
ge
CL
lai
attend
shang
take
ke
class
de
DE
xuesheng.
student
‘Everyone knows the three students who came to class.
OR: ‘Everyone knows three (possibly different) students who came to class.’
b. Mod-Num phrase [>3 : #;3 >:]
Mei
Every
ge
CL
ren
people
dou
DOU
renshi
know
lai
attend
shang
take
ke
class
de
DE
san
three
ge
CL
xuesheng.
student
‘Everyone knows the three students who came to class.
Not available: ‘Everyone knows three (possibly different) students who came to
class.
Nominal-internal word order also controls uniqueness, a novel observation. Consider the two
scenarios described in (5), which crucially differ by the number of groups of individuals in the
context that satisfy the predicate described by the nominal. In Scenario 1 (5a), there is one and
only one group of three students who regularly attended class. In Scenario 2 (5b), there are
multiple such groups, 10
3-many to be exact.
(5) a. Scenario 1 (unique):
There was a semantics class. Three students regularly attended. These three stu-
dents all passed the final exam.
b. Scenario 2 (non-unique):
The Modification Puzzle of Mandarin Numeral Phrases
There was a semantics class. Ten students regularly attended. Among these ten
students, only three passed the final exam.
A prenumeral modifier is preferred in Scenario 1, the unique scenario (6a), while postnumeral
modifier is preferred in Scenario 2, the non-unique scenario (6b). The postnumeral modifier
example (6b) interprets as an assertion that the set of students who regularly attended class and
passed the final exam has a cardinality of 3.
(6) a. Mod-Num phrase [Scenario 1:;Scenario 2: #]
lai shang ke
attend class
de
DE
san
three
ge
CL
xuesheng
student
tongguo
pass
le.
PFV
‘Three students who regularly attended class passed.
b. Num-Mod phrase [Scenario 1: #; Scenario 2:]
san
three
ge
CL
lai shang ke
attend class
de
DE
xuesheng
student
tongguo
pass
le
PFV
‘Three students who regularly attended class passed.
2. Classifiers with a partitive semantics
2.1. A semantics for pluralities
We first describe the necessary ingredients to work with pluralities. These are typical notions
in a Link (1983)-style analysis of pluralities. First, the sum operator is an idempotent,
commutative and associative binary operation over entities. For any set of entities X,LX
denotes the sum of all entities in X. The subpart relation is defined over entities as xyiff
there is some entity zsuch that xz=y. We say two entities overlap if they have a common
subpart, and write xyto mean xoverlaps with y”. An entity is said to be atomic iff it has no
subparts other than itself. We write Atom(x)to mean xis atomic.” For any set of entities X,
Xdenotes the transitive closure of Xunder . A partition over an entity xis a set Pof entities
such that LP=xand elements of Pare pairwise non-overlapping.
2.2. Why is postnumeral modification possible?
Before addressing the core question of how nominal internal word order influences the speci-
ficity feature of the noun, we take a detour to revisit an old puzzle: why can Mandarin nominals
be modified before combining with a numeral classifier? This problem arises from a popular
analysis (Chierchia, 1998a, b) of Mandarin nominals, which explains why classifiers are oblig-
atory for numeral quantification in Mandarin, as shown in (7).
(7) san
three
*(ge)
CL
xuesheng
student
‘three students’
Chierchia (1998a, b) proposes that Mandarin bare nouns like xuesheng ‘student’ express kinds
and have denotations of type s,e. A bare noun that expresses a kind Kdenotes a function
that maps each world to the sum of all instances of Kin that world (8a). Modifiers, including
numerals like san ‘three’, denote entity predicates and not kind predicates (8b), and thus cannot
combine with bare nouns. Classifiers like ge CL effectively convert kinds to entities (8c),
allowing classifier-bare noun combinations to further combine with modifiers.
(8) a. [[xuesheng ‘student’]] = λs.ιxe.student(s)(x)
b. [[san ‘three’]] = λxe.|x|=3
Jia Ren—Qiuhao Charles Yan—Satoru Ozaki
c. [[ge CL]] = λxe.λye.yis an instance of the kind x.
This system does not allow modifiers to combine with bare nouns that have not combined with
a classifier yet, thus predicting postnumeral modifiers to be impossible in Mandarin. However,
postnumeral modification is common, grammatical and productive (Krifka, 1995):
(9) Postnumeral adjective
san
three
ge
CL
qinfen
diligent
de
DE
xuesheng
student
‘three diligent students’
(10) Postnumeral relative clause
san
three
ge
CL
lai
attend
shang
take
ke
class
de
DE
xuesheng
student
‘three students who came to class’
In fact, these kinds of modifiers do not even require classifiers:
(11) Adjective
qinfen
diligent
de
DE
xuesheng
student
‘students’
(12) Relative clause
lai
attend
shang
take
ke
class
de
DE
xuesheng
student
‘students who came to class’
This leaves us with the puzzle stated earlier: why can Mandarin nominals be modified before
combining with a numeral classifier?
2.3. Numerals need classifiers; modifiers do not
Sudo (2016) provides a different analysis of classifiers. His analysis targets Japanese, another
obligatory classifier language like Mandarin. According to his proposal, it is numerals, rather
than modifiers, that require classifiers; in other words, a numeral needs to combine with a
classifier first in order to combine with a bare noun, but modifiers do nott.
Sudo’s proposal is as follows. Numerals have been argued to be abstract entities (Rothstein,
2010; Scontras, 2014); in Sudo’s system, numerals have their own type, namely n. In addition,
the semantics of classifiers involves a sortal presupposition, which encodes various idiosyn-
cratic ontological requirements that classifiers impose on the nouns they combine with. For
example, Japanese rin is a classifier that can only be used with flowers. This requirement is
encoded as a presupposition in (13).
(13) [[rin]] = λs.λnn.λxe:flower(x)(s).|{yx:flower(y)(s)Atom(y)}| =n
The classifier takes a situation, a numeral, and a sum denoted by a bare noun. The number
phrase states that there exists a part of the sum with n.
The Modification Puzzle of Mandarin Numeral Phrases
2.4. Our semantics for classifiers
We now describe a partitive semantics of classifiers, which is based on Sudo’s system. To
model the ontological requirement each classifier enforces on the bare noun it combines with,
we propose that each classifier cdefines a set of partitions Partscover sums. For example, duo,
the Mandarin classifier for flowers, just like Japanese rin, might define Partsduo to be the set of
atomic partitions over sums of flowers. This proposal should work for mass noun classifiers as
well; for example, pin ‘bottle(s) of’ might define Partspin to be the set of partitions over sums
of liquid individuals, where the members in each partition are sums that occupy distinct bottles.
We expect there to be more precise definitions of Partscfor each classifier cwe have described
so far, but this doesn’t affect the validity of our overall proposal.
(14) a. Partsduo ={Pflower :zP.Atom(z) z1,z2P.z1 z2}
b. Partspin ={Pliquid :z1,z2P.z1 z2
zP.bbottle.contains(z)(b)
z1,z2P.bbottle.contains(z1)(b)
contains(z2)(b)z1=z2}
Our classifier semantics needs to be restricted by one principle in order for it to work with
numeral quantification. This is stated formally in (15), and it requires that no two partitions
defined by the same classifier give rise to different counts over the same sum.
(15) If cis a classifier, then for all sum x, it must be the case that for any two partitions
P
1,P
2Partscthat cover x, we have |P
1|=|P
2|.
The denotation for the Mandarin classifier ge is given in (16).
(16) [[ge]] = λs.λnn.λxe.λye:P.PPartsge yxy=MP
.P.PPartsge yxy=MP |P|=n
The classifier takes a situation s, a numeral n, and a sum xdenoted by a bare noun, and returns an
entity quantifier. The returned quantifier carries a presupposition which requires the existence
of a ge-style partition PPartsge that carves up x. The returned quantifier is a predicate true
of a sum yiff a Pthat satisfies the presupposition carves yinto nsums.
The proposal disassociates the presence of classifiers with the modification of bare nouns. As
languages like English, Mandarin bare nouns can freely be either predicative or argumental.
We now have a semantics for a numeral phrase that consists of a numeral, a classifier and a
bare noun, illustrated in (17). The denotation function on the first line is parametrized with
respect to a world or situation s.
(17) [[three CL student]]s
= [[[[3 [CL s]] student]]]s
= [[CL]](s)(3)(student)
=λye.P.PPartsge ystudent y=MP |P|=3
As seen in (17), three students in Mandarin has an existential meaning, roughly paraphrased as
“there exists a sub-plurality in the total sum of students with a cardinality of 3”. This phrase
can combine with a prenumeral modifier via Predicate Modification (Heim and Kratzer, 1998).
Jia Ren—Qiuhao Charles Yan—Satoru Ozaki
This is illustrated for the relative clause lai shangke de ‘who regularly attended class; lit. attend
class DE in (18).
(18) [[[attend class DE] [three CL student]]]
=λye.[[attend class DE]](y)[[three-CL-student]](y)
=λye.attend-class(y) P.PPartsge ystudent y=MP |P|=3
As for postnumeral modifiers, we propose that they still denote entity predicates of type e,t,
but they can modify kinds denoted by bare nouns via the help of a pair of operators known
as up () and down (; Chierchia (1998a, b)). These operators transfer meanings between the
types s,eand s,e,t⟩⟩. These operators are defined in (19), and an example derivation for
postnumeral modifiers is given in (20).
(19) =λxs,e.λss.λye.yx
=λxs,e,t⟩⟩.λss.M{y:x(s)(y)}
We write xfor (x)and xfor (y).
(20) [[[three CL [attend class DE] student]]]s
= [[CL]](s)(3)((λs
s.λye.[[attend class DE]](y)student(s)(y))(s))
=λye.P.PPartsge yattend-class student y=MP |P|=3
This kind of postnumeral modification is similar to a proposal by Krifka (1995), who suggests
that Mandarin bare nouns are modifiable concepts, because concepts are of type e.
Compare the Mod-Num example (18) and the Num-Mod example (20). The Mod-Num case
describes a predicate that is true iff there is a strict sub-plurality yof students such that y
attended class and has a cardinality of 3. This predicate can be satisfied no matter if there are
exactly three or more than three students who attended class. On the other hand, the Num-Mod
case describes a predicate that is true iff there is a strict sub-plurality yof students that attended
class such that yhas a cardinality of 3. This predicate can only be satisfied if there are more
than three students who attended class. This correctly predicts a pattern we described in Section
1 that only the Mod-Num example can be used in Scenario 1 (5a), a “unique” scenario where
there are exactly three students who attended class.
This leaves unexplained two contrasts. The first is the grammaticality contrast between the
Mod-Num case and the Num-Mod case in Scenario 2 (5b), the “non-unique” scenario. The
second, which in fact subsumes the first, is the specificity contrast between the two nominal-
internal orders. So far, our proposal predicts that unmodified numeral phrases are always non-
specific in Mandarin. This is a correct prediction, as confirmed below by the flexible opacity
and scope ambiguity of Mandarin numeral phrases (Carlson, 1977).
(21) wo
I
xiang
want
jian
see
san
three
ge
CL
xuesheng.
present student
‘I want to meet three students.
Or: ‘There are three specific students that I want to meet.’
(22) # Wo
I
fanfu
repeatedly
shadiao
kill
san
three
ge
CL
xuesheng.
student
The Modification Puzzle of Mandarin Numeral Phrases
Intended: ‘I killed students repeatedly.
We return to an explanation of the specificity contrast in Section 3.
2.5. Ruling out a non-restrictive relative clause analysis
A potential alternative analysis of the semantic contrast between pre- and post-numeral relative
clauses is to reduce it to a restrictivity difference between the two relative clauses: pre-numeral
relative clauses might be non-restrictive, while post-numeral ones might be restrictive. We
do not pursue this direction in this paper, mostly because it is difficult to diagnose whether
relative clauses that co-occur with numerals are restrictive or non-restrictive. Del Gobbo (2003,
2005) proposes certain diagnostics, but their validity has been questioned by Lin and Tsai
(2015). Further syntactic diagnostics proposed by Del Gobbo (2010) as well as semantic ones
proposed by Lin and Tsai (2015) work well with relative clauses modifying proper names, but
not those modifying numerally quantified nominals, which exclusively constitute the examples
of relative clauses we deal with in this paper. Thus, we leave exploring this alternative direction
to future research. For now, we assume with Del Gobbo (2010) and Lin and Tsai (2015) that
these prenominal relative clauses are not like English non-restrictive relative clauses, and we
will stick to treating these as restrictive relative clauses denoting non-presuppositional, non-
supplementary content.
3. High and Low Modifiers
What remains to be explained is why Mod-Num phrases have specific interpretations. Before
sketching out our analysis, we first point out a crucial structural difference between Num-Mod
and Mod-Num phrases. The difference is concerned with the position of the demonstrative
within the nominal configurations. As shown in (23), demonstratives are only able to appear
ahead of numerals rather than modifiers.
(23) a. <na>
that
san
three
ge
CL
<*na>
that
lai
come
shang
attend
ke
class
de
DE
xuesheng
student
‘the three students who came to class’ [Dem-Num-Mod]
b. <*na>
that
lai
come
shang
attend
ke
class
de
DE
<na>
that
san
three
ge
CL
xuesheng
student
‘the three students who came to class’ [Mod-Dem-Num]
In (23a), which is a Num-Mod phrase, the demonstrate na ‘that’ can occur before the numeral-
classifier sequence, but cannot stay in-between. In its Mod-Num counterpart (23b), the demon-
strative occupies the position between the modifier and the numeral, which still allows it to
precede the numeral in that position. However, putting the demonstrative in the nominal-initial
position right before the relative clause is ungrammatical within the same configuration.
What this distinction shows to us can also be interpreted in a different way with respect to
the position of modifiers. Here we term the relative clause in (23a) a low modifier due to its
nominal-internal position. By contrast, we term the relative clause in (23b) a high modifier
because it is external to the DP. This position-based dichotomy among nominal modifiers is
reminiscent of what Sa˘
g (2019) proposes for Turkish modified nominals.
In Turkish, nominal phrases with the classifier tane show similar specificity difference as what
we see in Mandarin noun phrases. When the nominal modifiers are relative clauses, they can
also appear in two different positions, either preceding the determiner (as well as the nominal)
Jia Ren—Qiuhao Charles Yan—Satoru Ozaki
or intervening between the determiner and the nominal. Sa˘
g (2019) differentiates the former
from the latter, respectively dubbing them outer and inner relative clauses. Crucially, when
Turkish noun phrases with classifier (e.g., tane) co-occur with outer relatives, they can be in-
terpreted as definites, but not when they are modified by inner ones. It is evident that such a
contrast is similar to what we have seen in Mandarin throughout the paper, namely that nu-
meral nominals with low modifiers (i.e., Num-Mod phrases) are non-specific, whereas those
with high modifiers (i.e., Mod-Num phrases) are specific. As already given in (23), in the for-
mer situation, the modifier follows both the demonstrative and the numeral; but in the latter
situation, the modifier is linearly before the demonstrative and the numeral at the same time.
Returning to Turkish modified nominals, Sa˘
g (2019) proposes that classifiers like tane has a
built in choice function variable, and that numeral phrases are indefnites of type e. Outer
relative clauses are merged directly above expressions of type ethrough nominalization, giving
rise to the specificity effect.
(24) [[tane f]] = λnn.λP.f(λxe.S.Π(S)(x) |S|=n sS.P(s)) (Sa˘
g, 2019)
Following Sa˘
g (2019), we propose a same line of analysis of the specificity effect that the Mod-
Num phrases display. Instead of assuming relative clauses to merge directly above expressions
of type evia nominalization, we suggest that the relative clause provides domain restriction
for the existential choice function. In this sense, the specificity interpretation comes from the
domain restriction.
(25) Structures for Mod-Num and Num-Mod phrases
4. Mandarin possessives
It is worth mentioning that the specificity contrast that we observe among numeral phrases is
not unique to those involving modifiers like relative clauses. We show that the same difference
regarding specificity is also found in other numeral constructions that contain possessors. For
example in (26), the nominal maoxianyi ‘sweater’ is preceded by both a possessor Zhangsan
The Modification Puzzle of Mandarin Numeral Phrases
and a numeral-classifier sequence san jian ‘three CL’. The surface difference lies in the word
order between these two elements: the possessor precedes the numeral-classifier sequence in
(26a), whereas their word order is reversed in (26b).
(26) a. Zhangsan
Zhangsan
de
DE
san
three
jian
CL
maoxianyi
sweater
Zhangsan’s three sweaters. [Poss-Num]
b. san
three
jian
CL
Zhangsan
zhangsan
de
DE
maoxianyi
sweater
Lit.: three Zhangsan’s sweaters [Num-Poss]
Interpretation-wise, these two numeral constructions also behave differently. According to
Yang (2005), (26b) is used when there are more than three contextually salient sweaters that be-
long to the possessor Zhangsan (that is, there are actually five sweaters belonging to Zhangsan,
and only three of them are salient in the context). By contrast, (26a) is preferred over (26b)
when there are exactly three contextually salient sweaters and they all belong to Zhangsan (that
is, in the same context another person Lisi may also have three sweaters, but they are not as
salient as Zhang’s) (also see Huang (1982) and Tang (1990) for similar discussion).
The contrast above suggests that, as with Mod-Num phrases, the so-called Poss-Num phrases
are also specific in nature; whereas those Num-Poss phrases are non-specific just like Num-
Mod ones. This idea seems to be on the right track, since it is further borne out by the specificity
diagnostics such as existential construction (27).
(27) a. *You
YOU
Zhangsan
Zhangsan
de
DE
san
three
jian
CL
maoxianyi
sweater
xiaoshi-le.
disppear-PF V
Lit.: ‘Zhangsan’s three sweaters disappeared. [Poss-Num]
b. You
YOU
san
three
jian
CL
Zhangsan
Zhangsan
de
DE
maoxianyi
sweater
xiaoshi-le.
disappear-PF V
‘There are three Zhangsan’s sweaters that disappeared. [Num-Poss]
If the Poss-Num phrases are specific, we predict that they cannot occur in the existential con-
struction. This is corroborated by the ungrammatical result in (27a). By contrast, as to the
Num-Poss phrases, since they are assumed to be non-specific, we do not hold the same pre-
diction regarding their occurrence in the same existential configuration. It follows that (27b) is
grammatical.
Since the numeral constructions involving possessors lead to the same result of specificity as
their counterparts containing modifiers, we generalize the nominal configurations in (28) with
respect to specificity: if a numeral (plus a classifier) is preceded by some constituent (e.g.,
adjective, relative clause, possessor, etc.), the resulting nominal phrase is specific; reversely,
if the same constituent follows the numeral (plus a classifier), the nominal phrase becomes
non-specific.
(28) a. X-Num-CL-NP [specific nominals]
b. Num-CL-X-NP [non-specific nominals]
The templatic configurations above capture all the specificity contrast among numeral phrases
that we have seen in this paper. It is very likely that our proposed analysis of the numerals with
Jia Ren—Qiuhao Charles Yan—Satoru Ozaki
modifiers can be extended to those with possessors.For the sake of space, we leave the detailed
extension of our analysis in future research.
5. Conclusion
In this paper we offered a semantic account for the interpretational differences that are ob-
served among nominal phrases with different internal word order. We demonstrate that when
a modifier and a numeral co-occur within a nominal, the relative word order between these
two pre-nominal elements gives rise to the specificity contrast (as well as the uniqueness of
the nominal). We build on the semantics of classifiers proposed by Sudo (2016) to explain the
non-specificity of Num-Mod phrases, and adapt Sa˘
g (2019)’s analysis of high/low modifiers to
account for the specificity that arises from Mod-Num phrases. Though our discussion through-
out the paper is mostly confined to the interaction between numerals and modifiers, we point
out the potentiality of extending our analysis to other nominal constructions that also display
the same specificity contrast, e.g., those involving possessors.
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Typologically speaking, adjectival expressions like relative clauses rarely precede a demonstrative in a pre-nominal position (cf. Greenberg 1963; Cinque 2005). The word order, nevertheless, is commonly observed among Chinese dialects. In fact, the division between restrictive and nonrestrictive relative clauses in Chinese has long been a controversial issue since Chao (1968) and Huang (1982), where a pre-demonstrative relative is considered restrictive, and a post-demonstrative relative non-restrictive (descriptive in Chao's terms). Contra Del Gobbo (2010), we argue against the idea of treating the relative clause marker de as a complementizer. One crucial reason is that a complementizer is never known to license extraction (as well as ellipsis). Instead, we propose that Chinese post-demonstrative relatives are situated in the SPEC of a ModP headed by de, which serves as a formal licenser in terms of sisterhood (cf. Tsai 2011). By contrast, pre-demonstrative adjectivals and relatives do not carry the same clout, which may be attributed to their adjunct status after remnant movement following nominal head raising (cf. Aoun & Li 2003). In terms of semantics, evidence shows that relatives modifying a proper name or pronoun possess more properties of restrictive relatives than those of nonrestrictive relatives. However, there are equally clear cases where a name-modifying relative is not used to restrict the reference of the proper name. We thus agree with Del Gobbo (2010) in that name-modifying relatives are a type of “integrated nonrestrictives”. This restrictive vs. nonrestrictive dilemma receives a plausible account under the treatment of proper names as predicates of type <e,t> just like common nouns. On the assumption that proper names are type <e,t> expressions, name-modifying relatives can be semantically computed via exactly the same rule of restrictive predicate modification proposed by Heim and Kratzer (1998).
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This article offers an account of the mass/count distinction and the semantics of count nouns, and argues that it is not based on an atomic/non-atomic nor on a homogeneous/non-homogeneous distinction. I propose that atomicity in the count domain is atomicity relative to a context k, where k is a set of entities that count as atoms (i.e. count as one) in a particular context. Assuming for simplicity Chierchia's (1998a) and Rothstein's (2004) theory of mass nouns, in which they denote atomic Boolean semi-lattices closed under the complete join operation, we define an operation COUNTk that applies to the mass noun denotation Nmass and derives the count noun meaning: a set of ordered pairs <d,k> where d is a member of N ∩ k and k is the context k relative to which the operation applied. So, there is a typal distinction between mass nouns, which are of type <d,t>, and count nouns, which are of type <d×k, t>. The grammatical differences between count and mass nouns follow from this typal distinction. This allows us to encode grammatically the distinction between semantic atomicity, that is, atomicity relative to a context k, and natural atomicity, that is, inherent individuability. We show a number of ways in which this distinction is grammatically relevant.
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One of the most lively and contentious issues in contemporary linguistic theory concerns the elusive boundary between semantics and pragmatics, and Professor Laurence R. Horn of Yale University has been at the center of that debate ever since his groundbreaking 1972 UCLA dissertation. This volume in honor of Horn brings together the best of current work at the semantics/pragmatics boundary from a neo-Gricean perspective. Featuring the contributions of 22 leading researchers, it includes papers on implicature (Kent Bach), inference (Betty Birner), presupposition (Barbara Abbott), lexical semantics (Georgia Green, Sally McConnell-Ginet, Steve Kleinedler & Randall Eggert), negation (Pauline Jacobson, Frederick Newmeyer, Scott Schwenter), polarity (Donka Farkas, Anastasia Giannakidou, Michael Israel), implicit variables (Greg Carlson & Gianluca Storto), definiteness (Barbara Partee), reference (Ellen Prince, Andrew Kehler & Gregory Ward), and logic (Jerrold Sadock, Francis Jeffry Pelletier & Andrew Hartline). These original papers represent not only a fitting homage to Larry Horn, but also an important contribution to semantic and pragmatic theory.
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IntroductionThe Logic of Plurals and Mass Terms (LPM)Applications to Montague GrammarNotes